Zeke Emanuel was the target of bilious commentary by British TV presenters over his participation in a 1981 reality show, Now Get Out of That. An early precursor of the Survivor programmes, the show featured students in an Oxford versus Cambridge challenge performing a variety of physical and mental tasks. At every turn the commentators had something really foul to say about Zeke — “pushy”, “volunteers for everything” and, after all, “an American”.

Though he says he has no TV and didn’t even see the programme until one of his daughters gave him a DVD of the show as a Chanucah present, Zeke Emanuel has plainly committed to memory the presenter’s conclusion: “Zeke may be pushy, but where would Oxford be without him?”

“Pushy” is the word that runs through Zeke Emanuel’s latest book like lettering in a stick of rock. For pushy, read in-your-face, loud, sweary Jewish brothers, who soared from a wild, rough-and-tumble Chicago childhood to become three of the most influential Americans of their generation. Zeke, eldest of the three Emanuels, was born in Tel Aviv in 1957 (“in Mendele Street”) and became President Obama’s health policy adviser in his first administration, from 2009-11. He is now chairman of the Department of Medical Ethics and Health Policy at the University of Pennsylvania, a distinguished oncologist whose books on euthanasia and the best end to life have contributed significantly to America’s national debate.

Next is Rahm, also famous in Obama’s first White House as chief of staff and apparently the inspiration for the West Wing’s Josh Lyman. Rahm is now Mayor of Chicago, slightly to his elder brother’s amusement. When Zeke goes to visit, the larger-than-life pictures of “Hizzoner” at O’Hare Airport leave no one in any doubt as to who is in charge. And the baby of the family is Ari Emanuel, Los Angeles-based and a Hollywood superagent, widely said to be the model for the foul-mouthed Ari Gold in the hit TV series, Entourage. Family get-togethers are the acme of rambunctious behaviour, all arm-waving, finger-pointing, and yes, much swearing.

Nevertheless, as Zeke tells it in his delicious memoir, Brothers Emanuel, no one, looking at the three boys as they left high school in Chicago, would have predicted that they were were set for greatness. He rejects the tag of “the Jewish Kennedys”, insisting that they were average students — in Ari’s case, almost below average, as the youngest brother had severe dyslexia and became one of the first children in America to take Ritalin as a way of dealing with his hyperactive behaviour.

But the story Zeke tells is at once fascinating and familiar, particularly to a Jewish readership. Benjamin, the boys’ father, was an Israeli immigrant to the US whose original family name was Auerbach. When his elder brother, Emanuel, died in 1933 after a stray bullet fired during Arab riots hit his leg, the grief-stricken parents changed their surname to Emanuel in his memory. Benjamin became a doctor whose almost first mention in the book is that “he broke his leg, dancing at a barmitzvah”. Marsha, the boys’ mother, was a Chicago native and a serious civil rights activist at a time when political demonstrations frequently escalated into violence. She bundled her children on to buses to stand shoulder-to-shoulder with her African-American friends. She had a clear sense, recalls Zeke, of what had to be done because it was right.

In Marsha’s eyes, there were ways to do things which permeated the household. “None of us brothers became believers in God,” writes Zeke, “but we are all deeply Jewish and take the practices seriously. Our children have gone to Jewish day school; each of us still makes Friday night dinners special and says all the requisite prayers. For us Judaism is a religion without a supreme authority like the Pope. Instead, it offers a tradition in which sages offer various interpretations and arguments about the meaning of every passage of the Bible. As a result we became imbued with the Jewish ethos of constantly challenging authority, asking questions, and examining every aspect of life.”

Perhaps questioning the tenets of Jewish law was an easier deal for the Emanuel brothers than Marsha’s decision to send all three of her wild child sons to… ballet classes. Difficult though it may be to believe, Rahm — later recognised as the hardest of political hardheads — became an excellent dancer and continued the classes long after Zeke and Ari had begged to be excused. He even parlayed that into his university education, attending Sarah Lawrence, a well-known liberal arts college, rather than a more formal academic setting.

For four years from just after the 1967 Six-Day War, the brothers spent every summer in Israel, a central part of their lives. “These were not so much vacations as a chance to live for a season as Israelis. We ate the local cuisine, played on the beaches, swam in the sea, shopped in the markets, and practised our Hebrew. On our first trip Ari, Rahm, and I fought with one another to see who would be the first to scuttle down the stairs that were brought up to the tail of the plane and stand on Israeli soil. I won. Even at age nine I understood the seriousness of history and the pride and joy represented by a Jewish state.” The close companionship of the three in Israel was, says Zeke, a core reason for their later closeness as adults.

He writes with great pride about the physical love administered by their parents — hugs and kisses wherever possible — to the extent that friends told Ben and Marsha that such affection was bound to turn the boys gay. But he is also clear that none of them could have achieved what they did had they stayed in Israel, which had been his mother’s dearest wish. “I probably would not have become a doctor, but would have gone into the military. Ari would hardly have become a superstar agent in Israel.” Rahm, he’s not sure about. He might have become a politician in Israel, too.

Zeke’s bittersweet account of his two years in Oxford during the bleak beginning of Thatcher’s Britain — with the dollar at a measly 2.40 to the pound and a broke Zeke unable to keep warm in his digs — has a slightly wistful quality. It was at Oxford that Zeke first studied under and then became great friends with biochemist Professor Raymond Dwek. And in Oxford that he got himself a criminal record. Crime? Riding, on his way back from photographing Professor Dwek’s son Robert’s barmitzvah, without a tail light on his bike. Fine, £175, which, with that exchange rate, the impoverished Zeke could not pay. Raymond Dwek, he records, paid the fine and allowed his student to work it off by teaching in the Oxford cheder and giving tutorials in biochemistry.

Writing the book — in which he is unstintingly honest about his own flaws — Zeke appreciates the opportunity to think about his family’s history and what each of them brought to the table. It wasn’t hard, he says, to get back into the skin of the wild nine-year-old he once was. “We really had a great time.”